This document discusses elementary signals that are basic building blocks for more complex signals in signal and systems analysis. It identifies six types of elementary signals: unit step, unit ramp, unit parabolic, unit impulse, sinusoidal, and real exponential sequences. Each signal type is defined, with the unit step existing only for positive time, the unit ramp increasing linearly over time, the unit parabolic following a quadratic function, and the unit impulse being equal to one only at time zero. The document also notes that sinusoidal sequences can be periodic or not depending on frequency, and that real exponential sequences grow, decay, or alternate based on their constant value.

1. Elementary Signals
By
Md. Fazle Rabbi
16CSE057

2. 4.2
Elementary Signal
 There are several elementary signals which play vital role
in the study of signals and systems.
 These elementary signals serve as basic building blocks for
the construction of more complex signals.
 These elementary signals are also called standard signals

3. 4.3
Types of Elementary Signals
1. Unit step sequence
2. Unit ramp sequence
3. Unit parabolic sequence
4. Unit impulse sequence
5. Sinusoidal sequence
6. Real exponential sequence

4. 4.4
UNIT STEP Sequence
The unit step sequence is an important
signal used for analysis of many discrete-
time systems.
It exists only for positive time and is zero
for negative time.

5. 4.5
UNIT STEP Sequence

6. 4.6
UNIT RAMP Sequence
The discrete-time unit ramp sequence r(n) is that
sequence which starts at n = 0 and increases
linearly with time and is defined as:

7. 4.7
UNIT PARABOLIC Sequence
The discrete-time unit parabolic sequence p(n) is
defined as:

8. 4.8
UNIT IMPULSE Sequence
The discrete-time unit impulse function delta(n), also
called unit sample sequence.
This means that the unit sample sequence is a signal
that is zero everywhere, except at n = 0, where its value
is unity. is defined as:

9. 4.9
SIMUSOIDAL Sequence
All continuous-time sinusoidal signals are periodic, but
discrete-time sinusoidal sequences may or may not be
periodic depending on the value of ὠ.
The discrete-time sinusoidal sequence is given by

10. 4.10
Real Exponential Sequence
The discrete-time real exponential sequence 𝑎𝑛is
defined as:
• a > 1, the sequence grows exponentially as
shown in Figure (a).
• 0 < a < 1, the sequence decays exponentially
as shown in Figure (b).
• a < 0, the sequence takes alternating signs as
shown in Figure [(c) and (d)].

11. 4.11
Real Exponential Sequence

12. 4.12
Thank You